Characteristic Features of the Rhodium Stereochemistry in the Structure of Carbonyls and Organometallic Compounds

Characteristics of the Voronoi–Dirichlet polyhedra (VDP) were used to carry out crystal chemical analysis of 160 compounds containing 308 RhC _n or RhC _n Rh _m coordination polyhedra. The volume of the rhodium VDP virtually does not depend on the coordination number (C.N.), which varies from 4 to 12, in spite of the pronounced variation of the Rh–C (1.72–2.83 Å) and Rh–Rh (2.55–2.97 Å) bond lengths. It is shown that the VDP parameters allow one to estimate quantitatively the main features of rhodium stereochemistry irrespective of the nature (Rh or C) and the number (n varies from 3 to 12 and m varies from 0 to 6) of atoms in the first coordination sphere.     

The coordination polyhedra KCl<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript> in the crystal structures

The Voronoi-Dirichlet polyhedra (VDP) and the method of intersecting spheres were used to carry out crystal chemical analysis of 141 chlorides containing 245 crystallographic sorts of potassium atoms in the KCl_n coordination polyhedra. The potassium atoms in the crystal structures can coordinate 6 to 12 chlorine atoms, the K-Cl bond lengths varying from 2.81 to 3.91 Å. The radius of spherical domains whose volume coincides with the volume of potassium VDP was found to be virtually independent of the coordination number or the shape of the coordination polyhedron, being equal to 1.93(4) Å. The VDP characteristics were used to analyze the stereochemical features of potassium in the crystal structures.Translated from Koordinatsionnaya Khimiya, Vol. 31, No. 1, 2005, pp. 72–80.Original Russian Text Copyright © 2005 by Bikanina, Shevchenko, Serezhkin     

The Coordination Polyhedra PdX n (X = Cl,Br, I) in Crystal Structures

The Voronoi–Dirichlet polyhedra (VDP) and the method of intersecting spheres were used to perform crystal-chemical analysis of 106 compounds containing palladium atoms surrounded by halogen atoms. Depending on the oxidation number (2 or 4), Pd atoms can bind 4 to 6 X atoms (X = Cl, Br, I) and form PdX _n coordination polyhedra shaped like octahedra or square pyramids (n = 6), square pyramids (n = 5), or squares (n = 4). A lone electron pair on Pd(II) was found on the basis of X-ray diffraction data. The influence of the palladium valence state on the key stereochemical features of palladium halide complexes is considered in terms of the 18-electron rule. The tendency of palladium atoms to Pd···H aghostic interactions was noted.     

The SmO n Coordination Polyhedra in Crystal Structures

Crystal-chemical analysis of all compounds studied to date and containing SmO _n coordination polyhedra was performed using the methods of Voronoi–Dirichlet polyhedra (VDP) and intersecting spheres. It was shown that the coordination number (CN) of Sm(III) atoms with respect to oxygen varies from 4 to 12 and the CN of Sm(II) is 5, 7, or 9. The Sm(III) Sm(II) transition was found to entail an increase in the VDP volume by, on average, 2.8 ų, whereas for a constant oxidation state of Sm, the VDP volume barely depends on the CN, although the Sm–O interatomic distances vary by 0.83 Å for Sm(III)-containing crystals and by 0.39 Å for Sm(II)-containing crystals. The results of analysis of the topology of [Sm _a O _b ] groups in the crystal structure are presented.     

The coordination polyhedra GaS<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript> in crystal structures

Voronoi-Dirichlet polyhedra (VDP) and the intersecting sphere method were used to perform coordination analysis of 204 crystallographically different gallium atoms in the structures of all known compounds containing GaS _n polyhedra. The Ga(III) atoms in crystal structures were found to be linked to 6, 4, or three sulfur atoms to form coordination octahedra, tetrahedra, and triangles, respectively, whereas Ga(II) atoms are bound only to three sulfur atoms and a gallium atom. The effect of the valence state and the coordination number of gallium atoms on the key parameters of the VDP is considered. A common linear dependence of the solid angles of the VDP faces corresponding to the Ga-S bonds on the corresponding interatomic distances, which vary from 2.09 to 2.53 Å, was established to exist.     

Manganese Stereochemistry in the Structures of Oxygen-Containing Compounds

The Voronoi-Dirichlet polyhedra (VDP) and the method of intersecting spheres were used to carry out crystal chemical analysis of coordination of 1304 sorts of Mn atoms in the structure of 859 oxygen-containing compounds. The manganese atoms whose oxidation number varies from 2 to 7 were found to bind 4 to 8 oxygen atoms giving rise to the MnO _n coordination tetrahedra (n = 4), square pyramids (n = 5), octahedra or trigonal prisms (n = 6), pentagonal bipyramids or one-cap trigonal prisms (n = 7), trigonal dodecahedra, cubes, square antiprisms, or hexagonal bipyramids (n = 8). The effect of the valence state and the coordination number of manganese atoms on the parameters of their VDP was studied. The existence of a general linear correlation between the solid angles of the VDP faces corresponding to Mn-O bonds and the corresponding interatomic distances, which vary over a broad range (1.55–3.12 Å), was established. The VDP characteristics can be used to determine the valence state of Mn atoms in the crystal structures and in the crystal chemical analysis of manganites with giant magnetoresistance.     

Coordination polyhedra LnOn (Ln = Er, Tm, Yb, Lu) in crystal structures

The Voronoi-Dirichlet polyhedra (VDP) and the method of intersecting spheres were used to analyze crystal structures of 728 compounds containing 976 crystallographically non-equivalent sorts of LnO_n polyhedra (Ln = Er, Tm, Yb, Lu). The Ln C.N. vary from 3 to 10, and 14 sorts of coordination polyhedra are present in the structures. Despite the great diversity of C.N., the volume of the VDP was found to depend only on the nature of the Ln atom and its valence state.     

Coordination Polyhedra RhX6 (X = F,Cl, Br) in Crystal Structures

Voronoi–Dirichlet polyhedra (VDP) and the method of intersecting spheres were used to perform crystal-chemical analyses of compounds containing complexes [Rh _a X _n ] ^z– (X = F, Cl, Br). It was found that, irrespective of oxidation number (+3, +4, or +5), rhodium atoms always exhibit the coordination number 6 with respect to the halogen atoms and have octahedral coordination. The influence of site symmetry and the valence state of Rh on the distortion of RhX₆ octahedra are considered. The electronic configuration of the Rh atoms is shown to influence the symmetry of their valence-force field within the crystal structure.     

Coordination Polyhedra TiOn in Crystal Structures

The Voronoi–Dirichlet polyhedra (VDP) and the method of intersecting spheres were used to perform crystal-chemical analysis of 532 compounds containing 940 crystallographic sorts of titanium atoms in TiO _n coordination polyhedra. It was found that Ti(IV) or Ti(III) atoms can coordinate four to eight oxygen atoms. For a constant valence state and a constant coordination number (C.N.) of titanium, the Ti–O bond lengths vary by 0.1–1.0 Å. At C.N. #gt; 5, the volume of the metal VDP remains virtually unchanged; when the C.N. decreases to 4, the VDP volume increases by 2–3 ų. For a constant C.N., Ti(IV) Ti(III) transition is accompanied by an increase in the VDP volume of metal atoms of 0.5–1.9 ų. The VDP characteristics of the Ti atoms can be used to determine their valence state and to identify the titanium–metal bonds in the structures of compounds.     

The coordination polyhedra ZnS<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript> in crystal structures

Voronoi-Dirichlet polyhedra (VDP) and the intersecting sphere method were used to analyze the coordination of zinc atoms in the structures of all known compounds containing ZnS _n polyhedra. The Zn(II) atoms were found to coordinate 6, 5, 4, 3, or 2 sulfur atoms to form coordination octahedra or trigonal prisms (n = 6), trigonal bipyramids (n = 5), tetrahedra (n = 4), triangles ZnS₃, or dumbbells ZnS₂. The effect of the coordination number of zinc atoms on the key parameters of zinc VDP is considered. A common linear dependence of the solid angles of the VDP faces corresponding to both valence and non-valence Zn-S contacts on the interatomic distances was established to exist. Although the Zn-S bond lengths vary over a broad range (2.39 to 3.29 Å), the Zn VDP volume almost does not depend on its C.N. with respect to sulfur. Some characteristic features of Zn stereochemistry are considered from the 18-electron rule standpoint.     

The IrX6 Coordination Polyhedra (X = F,Cl, Br) in Crystal Structures

The Voronoi–Dirichlet polyhedra (VDP) and the method of intersecting spheres were used to perform crystal-chemical analysis of compounds containing [Ir _a X _b ] ^z– complexes (X = F, Cl, or Br). The coordination number of Ir atoms with respect to halogen atoms was found to be 6, irrespective of the oxidation state (III, IV, or V), and the coordination polyhedra formed by Ir were found to be always octahedra. The influence of the site symmetry and the valence state of the Ir atoms on the distortion of the IrX₆ octahedra is considered. It is shown that characteristics of the VDP of Ir atoms can be used for quantitative estimation of the crystal-chemical role of Ir atoms in the halide structures.     

The coordination polyhedra CdS<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript> in crystal structures

Voronoi-Dirichlet polyhedra (VDP) and the intersecting sphere method were used to perform analysis of coordination of cadmium atoms in the structures of all known compounds containing CdS _n polyhedra. The Cd(II) atoms were found to coordinate 6, 5, 4, or 3 sulfur atoms to form coordination octahedra or trigonal prisms, trigonal bipyramids, tetrahedra, or triangles, respectively. The effect of the coordination number of cadmium atoms on the key parameters of Cd VDP was considered. A common linear dependence of the solid angles of the VDP faces corresponding to both valence and non-valence Cd-S contacts on the corresponding interatomic distances was established to exist. Although the Cd-S bond varies over a broad range, from 2.39 to 3.29 Å, the Cd VDP volume almost does not depend on its C.N. with respect to sulfur.     

The EuOnCoordination Polyhedra in Crystal Structures

The Voronoi–Dirichlet polyhedra (VDP) and the method of intersecting spheres were used to perform crystal-chemical analysis of the compounds studied to date containing EuO _n polyhedra. The Eu(III) and Eu(II) atoms were found to have coordination numbers (C.N.s) from 6 to 12 with respect to oxygen. The Eu(III) Eu(II) transition entails an increase in the VDP volume by, on average, 4 ų. For a constant valence state of europium, the VDP volume barely depends on the C.N., although the Eu–O interatomic distances change by 0.72 Å for Eu(III)-containing structures and by 0.59 Å for Eu(II)-containing structures.     

Maximum filling principle and sublattices of actinide atoms in crystal structures

The most important characteristics of the Voronoi-Dirichlet polyhedra (VDP) of A atoms (A is actinide) in chemically homogeneous sublattices in the crystal structures of 3479 inorganic, coordination, and organometallic compounds are determined. The effect of the actinide nature on the A-A interatomic distances in the crystal structures is considered. In the Th, U, Np, or Pu sublattices, VDP have most often 14 faces and the Fedorov cuboctahedron is the most abundant type of VDP, whereas in Ac, Pa, Am, Cm, Bk, or Cf sublattices, the VDP have mainly 12 faces and are shaped like rhomobododecahedra. In A sublattices that typically form VDP with 14 faces, the actinide atoms occupy, most often, sites with C ₁ symmetry (47 to 59% of the sample size). In the case of actinides whose A sublattices tend to form VDP with 12 faces, the C ₁ site symmetry is found either very rarely (Pa, Am, Cf) or not at all (Ac, Cm, Bk).     

Coordination polyhedra LnCl n (Ln = La-Lu) in crystal structures

The Voronoi-Dirichlet polyhedra (VDP) and the method of intersecting spheres were used to analyze 125 compounds containing 182 crystallographically nonequivalent sorts of LnCl _n complexes (Ln = La-Lu). The lanthanum C.N. varies from 6 to 10; eight sorts of coordination polyhedra are encountered in the structures, the Ln-Cl bond lengths in which can vary by 0.1–0.8 Å, depending on the C.N.(Ln). Despite the great diversity of C.N. and large scatter of bond lengths, the volume of the VDP was found to depend only on the nature of the Ln atom and its valence state     

The OsX n Coordination Polyhedra (X = O,S, Se,Te) in Crystal Structures

The Voronoi–Dirichlet polyhedra (VDP) and the method of intersecting spheres were used to perform a crystal-chemical analysis of compounds whose structures contain Os atoms surrounded by chalcogen atoms. Depending on the valence state, Os atoms bind four to seven X atoms (X = O, S, Se, Te) forming OsX _n coordination polyhedra which can be tetrahedra (n = 4), trigonal bipyramids or square pyramids (n = 5), octahedra (n = 6), or pentagonal bipyramids (n = 7). In some compounds, pairs of OsO₆ octahedra share edges to form Os–Os bonds. The influence of the Os valence state and the nature of the chalcogen atom on the composition and structure of the [Os _a X _b ] groups is discussed. On the basis of analysis of the crystal-structural data from the standpoint of the 18-electron rule, dependences of the Os–O and Os–Os bond orders on the bond lengths are proposed.     

Maximum filling principle and sublattices of lanthanide atoms in crystal structures

The most important characteristics of the Voronoi-Dirichlet polyhedra (VDP) were determined for 20526 Ln atoms (Ln = La?Lu) in sublattices containing chemically identical lanthanide atoms in the crystal structures of 14659 inorganic, coordination, and organoelement compounds. The number of lanthanide VDP faces in the sublattice can vary from 4 to 36 and, irrespective of the lanthanide nature, the VDP have most often 14 faces. The Fedorov cuboctahedron is the most abundant type of VDP. In the crystal structures, Ln atoms were found to have, most often, C ₁ site symmetry (～49% of cases) and also C _s (16), C _2v (7%), or C ₂ (6%) site symmetries.     

Features of intermolecular interactions in the crystals of metal acetylacetonates

For 12 acetylacetonates of the composition M(acac) _n (n = 2, 3, or 4) and M(acac)(C₂H₄)₂ (M is a metal) the total area (⁰ S) of the faces of Voronoi-Dirichlet polyhedra (VDP) corresponding to all intermolecular contacts of one molecule in the crystal structure and the total volume of pyramids (⁰ V), whose bases are formed of such faces and the vertices are occupied by the nuclei of atoms participating in intermolecular contacts, are determined. The key features of non-bonded interactions are considered. The existence of a linear dependence of the sublimation enthalpy of acetylacetonates on the ⁰ S or ⁰ V parameters of their molecular VDP is revealed. It is shown that the sublimation enthalpy of Ga(acac)₃ requires the refinement and theoretically should be 124 kJ/mol.